"The government can not demonstrate the flexibility necessary for a successful deal if its hands are tied midway through that process", Davis said.

In parliament, May told lawmakers she had agreed with Brexit minister David Davis to "bring forward an amendment in the (House of) Lords". The strained parliament session underlined deep divisions over Britain's European Union exit. Brexiteers fear it is a Trojan horse to frustrate Brexit and bind the prime minister's hands.

Asked on Sky News about discussions on changes proposed by senior pro-EU Tory Dominic Grieve, Conservative vice-chairman Chris Skidmore said only that they "may lead to an amendment next week".

The vote on Tuesday is the first of two days of debate that will test May's authority and her plans for leaving the EU.

"The Brexit secretary [David Davis] has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and government in negotiating global treaties, and respecting the referendum result".

Ukip leader Gerard Batten said: "The only "meaningful vote" was the verdict of the people in referendum of June 23 2016".

Pro-European Conservative, Nicky Morgan, told the BBC that May understands that "parliament wants to have a real say, in all circumstances".

"She said that anything which undermines the government at home would make the negotiations with the European Union more hard".

Both Houses of Parliament must agree on the form of the EU Withdrawal Bill, and if the Lords insist on their amendment then the Commons will again be invited to reject it.

In particular, MPs voted 324 votes to 298 to reject a Lords amendment which would have strengthened parliament's statutory "meaningful vote" on the final deal between the United Kingdom and the EU.

The votes tonight followed a dramatic day of politics in Westminster on Tuesday, when Prime Minister May agreed in principle to give MPs greater power in the Brexit process in order to avoid a humiliating defeat. "We will now work with the government to get acceptable amendments tabled in the Lords to address this".

'The government's amendment today provides for a meaningful vote'.

It also imperils the now invisible border between the U.K.'s Northern Ireland and the Republic of Ireland, an European Union member.

The UK justice minister Philip Lee has resigned from the government to speak out against the government's policy on Brexit.

British Prime Minister Theresa May is urging feuding Conservative lawmakers to unite and prevent the government from being defeated in key votes on its main Brexit bill.

The bill repeals the 1972 laws that made Britain a member of the European community, and also copies and pastes EU laws into British statute books to smooth out regulatory transitions.

A separate vote against the Lords customs union amendment was rejected by 325 votes to 298, at a majority of 27. She now relies on the support of a small Northern Irish party.

Labour MP Chuka Umunna was among the rebels who defied a three-line whip and voted for the amendment.

Perhaps the most significant compromise from Mrs May was on what happens if there's no deal.